Expert answers to "Derivatives Evaluate the following derivatives. ddx(ln3(3x2+2))"

Jason Yuhas

Answered question

2022-01-17

Derivatives Evaluate the following derivatives.

\frac{d}{d x} (\ln^{3} (3 x^{2} + 2))

Marcus Herman

Beginner2022-01-18Added 41 answers

Step 1
To compute the derivative

\frac{d}{d x} (\ln^{3} (3 x^{2} + 2))

Use chain rule to find the derivative.
Step 2

\frac{d}{d x} (\ln^{3} (3 x^{2} + 2)) = 3 (\ln^{2} (3 x^{2} + 2)) \times \frac{d}{d x} (\ln (3 x^{2} + 2))

= 3 (\ln^{2} (3 x^{2} + 2)) \times \frac{1}{3 x^{2} + 2} \times 6 x

= \frac{18 x (\ln^{2} (3 x^{2} + 2))}{3 x^{2} + 2}

jean2098

Beginner2022-01-18Added 38 answers

{[\ln^{3} (3 x^{2} + 2)]}^{'} = {[{(\ln (3 x^{2} + 2))}^{3}]}^{'}

= 3 {(\ln (3 x^{2} + 2))}^{2} \cdot {(\ln (3 x^{2} + 2))}^{'}

= 3 {(\ln (3 x^{2} + 2))}^{2} \cdot \frac{1}{3 x^{2} + 2} \cdot {(3 x^{2} + 2)}^{'}

= 3 {(\ln (3 x^{2} + 2))}^{2} \cdot \frac{1}{3 x^{2} + 2} \cdot 6 x =

= \frac{18 x}{3 x^{2} + 2} \cdot {[\ln (3 x^{2} + 2)]}^{2}

Result:

\frac{18 x}{3 x^{2} + 2} \cdot {[\ln (3 x^{2} + 2)]}^{2}

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